Observational evidences for the existence of 17.4 keV decaying degenerate sterile neutrinos near the Galactic Center

Recent results from Chandra indicate that soft (∼ 0.8 keV) and hard (∼ 8 keV) hot gas components exist within the inner 20 pc of the Galactic Center (GC) (Park et al. 2003;Muno et al. 2004). The power needed to maintain the temperatures of the soft and hard components of the hot gas are 3 × 10 36 erg s -1 and 10 40 erg s -1 respectively. The energy needed for the soft component can be explained by 1% of kinetic energy from one supernova occurring every 3000 years, which is reasonable in the GC (Muno et al. 2004). However, the energy needed for the hard component cannot be explained satisfactorily (Muno et al. 2004). Chan and Chu (2008) proposed that a decaying sterile neutrino halo existing near the GC can solve the problem. The photons emitted by the decays of the sterile neutrinos can heat up the surrounding gas, and the energy is subsequently transferred to the entire region at the GC. For this scenario to account for the observational data, the sterile neutrino rest mass is required to be m s ≈ 16 -19 keV (Chan and Chu 2008). Recently, Suzaku X-ray mission has started to observe emission lines above 6 keV near the GC (Koyama et al. 2007;Nobukawa et al. 2010). The observed intensities of the emission lines, including Lyα (7.0 keV), Lyβ (8.2 keV) and Lyγ (8.7 keV), from Fe XXVI are 1.66 +0.09 -0.11 × 10 -4 ph cm -2 s -1 , 2.29 +1.35 -1.31 × 10 -5 ph cm -2 s -1 and 1.77 +0.62 -0.56 × 10 -5 ph cm -2 s -1 respectively (Koyama et al. 2007). Based on these results, Prokhorov and Silk (2010) find an excess of Lyγ intensity of (1.1 ± 0.6) × 10 -5 ph cm -2 s -1 , which cannot be explained by ionization and recombination processes. Prokhorov and Silk (2010) proposed that decaying sterile neutrinos can provide the excess 8.7 keV photons. As the emitted photon energy E s ≈ m s /2, the required m s is about 17 keV, which agrees with Chan and Chu's prediction (2008). By using the observed excess intensity of 8.7 keV photons and the Navarro-Frenk-White (NFW) density profile with 21.5 kpc scaled length to model the sterile neutrino halo, which means that the sterile neutrinos are the dominant dark matter component, Prokhorov and Silk (2010) calculated the sterile neutrino decay rate and mixing angle with active neutrinos to be Γ = (9.0±4.8)×10 -28 s -1 and sin 2 2θ = (4.1±2.2)×10 -12 respectively. However, there is no evidence that the density profile of the sterile neutrino halo behaves like the NFW profile. If the sterile neutrinos are degenerate, the size of the halo can be very small (radius R s < 1 pc) (Bilic et al. 2001;Chan and Chu 2007). In this article, we extend our earlier work to account for the high temperature of the hot gas near the GC by including into the consideration of the Suzaku excess of 8.7 keV photons; we show that the existence of a degenerate halo of decaying sterile neutrinos can account for both simultaneously (Chan and Chu 2008). In this model, the optically dense gas clouds inside and nearby the sterile neutrino halo absorbs most of the energy of the photons emitted by the decays of the sterile neutrinos. The energy is then transferred to the surrounding gas clouds by conduction (mean free path ∼ 2 pc). Since the optical depth is larger than 1, only a small portion of the decayed photons can escape from the GC and constitute the excess 8.7 keV emission. The calculated emission intensity from the decaying sterile neutrinos agrees with the observation as well as that required by Prokhorov and Silk (2010). In this scenario, the sterile neutrino decay rate Γ ≥ 5 × 10 -20 s -1 and mixing angle sin 2 2θ ∼ 10 -3 -10 -4 , which are consistent with a low reheating temperature and suggest that sterile -active neutrino oscillation may be visible in near future experiments.

Sterile neutrinos may decay into active neutrinos and photons (ν s → ν a +γ). The energy of the photons is assumed to be E s = 8.7 keV. Therefore, m s ≈ 2E s = 17.4 keV. Since the size of a degenerate sterile neutrino halo with total mass M s ≤ 10 6 M ⊙ and m s ≈ 17 keV is much smaller than 20 pc, the total energy flux of the decayed photons within the field of view of Suzaku (solid angle Ω) is given by

where r 0 = 8.5 kpc is the distance to the GC and P = M s Γc 2 /2 = 10 40 erg s -1 is the total power emitted in the sterile neutrino decays (the required power of the hard component of the hot gas near GC). The excess energy flux observed by Suzaku is F ′ s = (1.1 ± 0.6) × 10 -5 E s ≈ (1.5 ± 0.8) × 10 -13 erg cm -2 s -1 . Therefore, only around 1% of photons can escape from the GC, and most of the emitted photons are first absorbed by the gas clouds inside the sterile neutrino halo and nearby. The optical depth τ is given by

where σ i is the effective absorption cross section of 8.7 keV photons by different gas components including cold molecular hydrogen gas (i =H 2 ), warm atomic gas (i=H, He) hot ionized gas (i=hot) and very hot ionized gas (i=vhot), n i is the number density of the gas components. Assuming all the gas compon

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